Simplify. Rewrite the expression in the form $8^n$. $8^6\cdot 8^4=$
Explanation: $\begin{aligned} 8^6\cdot 8^4&=8^{6+4} \\\\ &=8^{10} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 8^6\cdot 8^4&=\underbrace{8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8}_\text{6 times}\cdot\underbrace{8\cdot 8\cdot 8\cdot 8}_\text{4 times} \\\\\\ &=\underbrace{8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8\cdot 8}_\text{10 times} \\\\ &=8^{10} \end{aligned}$ In conclusion, $8^6\cdot 8^4=8^{10}$.